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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

2. Volumes of Cones

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Exercise 6 Page 435

Use the formula for the volume of a cone.

1.5in

Practice makes perfect

We want to find the height of the given cone.

To do so, we can use the formula for the volume of a cone. V=1/3 B h Here, B is the area of the base and h is the height of the cone. Since the base is a circle, the area of the base will be equal to π r^2, where r is the radius. V= 1/3 π r^2 h We are given that the volume of the cone is 18π cubic yards and the radius of the base is 6 yards. Let's substitute these values into the formula and solve it for h.

V=1/3π r^2 h

V= 18π, r= 6

18π=1/3π ( 6)^2 h

▼

Solve for h

Calculate power

18π=1/3π(36)h

CommutativePropMult

Commutative Property of Multiplication

18π=1/3(36π h)

MoveRightFacToNumOne

1/b* a = a/b

18π=36π h/3

Calculate quotient

18π=12π h

.LHS /12π.=.RHS /12π.

18π/12π=12π h/12π

Cross out common factors

18π/12π=12πh/12π

Calculate quotient

18/12=h

Rearrange equation

h=18/12

Use a calculator

h=1.5

The height of the cone is about 1.5 inches.

Subchapter links

Try It p.434-435

Self-Assessment for Concepts & Skills p.435

Self-Assessment for Problem Solving p.436

Review & Refresh p.437

Concepts, Skills, & Problem Solving p.437-438